Einstein-Weyl structures on lightike hypersurfaces
Differential Geometry
2007-05-23 v1
Abstract
We study Weyl structures on lightlikes hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for ambiant Lorentzian space and a totally umbilical screen foliation, there is a strong interplay with the induced (Riemannian) Weyl-structure on the leaves. Finally, we establish necessary and sufficient conditions for a Weyl structure defined by the form of an almost contact structure given by an additional complex structure in case of an ambiant Kaehler manifold to be closed.
Cite
@article{arxiv.0704.3383,
title = {Einstein-Weyl structures on lightike hypersurfaces},
author = {Cyriaque Atindogbe and Lionel Bérard Bergery},
journal= {arXiv preprint arXiv:0704.3383},
year = {2007}
}